There are several new ingredients in the construction of our score statistic. First, the score function is derived based on a smoothed surrogate loss to overcome the nonregularity due to the nonsmoothness of the 0-1 loss. Second, unlike the existing works on high-dimensional inference, the score function from the smoothed surrogate loss is biased. By explicitly estimating the bias term, we derive the bias corrected score. Third, the decorrelation step, developed by [1]} for regular models, is applied to reduce the uncertainty of estimating high-dimensional nuisance parameters. Theoretically, we show that under some conditions, the proposed score test statistic converges in distribution to a standard Gaussian distribution under the null hypothesis. We further establish the local asymptotic power of the test statistic when \(\theta ^*\)  deviates from 0 in a local neighborhood. In particular, we give the conditions under which the test statistic has asymptotic power one.
